Geodesic
$W$-graph ideals and biideals
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 237-275.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We further develop the theory of $W$-graph ideals, first introduced in R. B. Howlett and V. M. Nguyen [J. Algebra 361, 188--212 (2012; Zbl 1271.20002)]. We discuss $W$-graph subideals, and induction and restriction of $W$-graph ideals for parabolic subgroups. We introduce $W$-graph biideals: those $W$-graph ideals that yield $(W\times W^{\mathrm{o}})$-graphs, where $W^{\mathrm{o}}$ is the group opposite to $W$. We determine all $W$-graph ideals and biideals in finite Coxeter groups of rank 2.
Classification : 05E10, 05C25, 20F55, 20C08
Keywords: Coxeter groups, Hecke algebras, $W$-graphs, Kazhdan-Lusztig polynomials, cells 
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Howlett, Robert B.; Nguyen, Van Minh. $W$-graph ideals and biideals. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 237-275. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a0/